1. Field to Which the Invention Relates
The invention relates to an interpolating non-recursive digital filter for generating output signal samples which occur at a given output sampling frequency f.sub.2 and which are related in a predetermined way to a sequence of input signal samples which occur at an input sampling frequency f.sub.1, f.sub.2 being an integer multiple r of the frequency f.sub.1, comprising: means for storing a sequence of N input signal samples x(nT), x[(n-1)T], x[(n-2)T], . . . x[(n-N+1)T] where n represents the number of the signal sample which occurred after the instant t=0; multiplying the adder means for generating within an input sampling period T=1/f.sub.1 a set of r successive output signal samples y[(n+m/r)T] where m = 0, 1, 2, . . . r-1, the relation between the N input signal samples and an output signal sample being expressed by ##EQU1##
In this equation r is the interpolation factor and a(m,0), a(m,1), a(m,2), . . . a(m,N-1) are elements of a set of multiplying coefficients a[m,k] of r mutually different sets of multiplying coefficients, each comprising N elements.
In what follows hereinafter the sets of coefficients will be designated with square brackets as a[m,k] and the elements of such a set with round brackets as a(m,k).
2. Description of the Prior Art
In chapter (D) a number of references are specified in which interpolating non-recursive digital filters are described. As is described more particularly for the interpolating digital filter indicated in reference 3, the N input signal samples are stored in, for example, a circulating delay line and the sets of multiplying coefficients a[m,k] where m = 0, 1, 2, . . . r-1 have been stored in a storage device such as, for example, an ROM. Under the control of an address code a set of multiplying coefficients which is characterized by a given value of m is read from the ROM and supplied to the multiplying means. The multiplying means now supply a set of sub-products of the form: a(m,0).x(nT), a(m,1).x[(n-1)T], a(m,2).x [(n-2)T]. . . . . . a(m,N-1). x[(n-N+1)T]. The sub-products belonging to such a set are subsequently added together by the adder means such as, for example, an accumulator so that the output signal sample y [(n+m/r)T] is obtained. After this signal sample has been read from the accumulator the latter is reset to its zero position and thereafter a new set of multiplying coefficients a[m+1,k] is read from the ROM for generating the output signal sample y[(n+(m+1)/r)T]T] whereafter the above process is repeated. When the output sampling frequency is increased by a factor r (r being an integer and exceeding (1) relative to the input sampling frequency the above described processing of the stored N input samples is repeated for each of the r sets of multiplying coefficients. Thereafter a new input signal sample x[(n+1)T] is written into the storage device, and the oldest input signal sample x[(n-N+1)T] disappears from the storage device. For generating the output signal samples y[{(n+1)+m/r}T] where m = 0, 1, 2, . . . r-1 the above processes are performed on the new sequence of N input signal samples x[(n+1)T], x(nT), x[(n-1)T], . . . x[(n-N+2)T].
For performing the processing of the input signal samples in a fully digitalized digital filter the input signal sample x(nT) as well as the multiplying coefficients a(m,k) are usually numbers in the binary system. Consequently also the output signal samples y[(n+m/r)T] are numbers in the binary system.
More particularly the numbers x(nT) represent samples of an analog information signal which has been sampled in the usual manner with the input sampling frequency f.sub.1 which samples have been quantized in a quantizer and thereafter converted to the code word x(nT).
As has been described in detail in ref. 3 the sets of multiplying coefficients a[m,k] where m = 0, 1, 2, . . . r-1 represent coded samples of the impulse response of the filters to be realized. In the interpolating case, the impulse response is sampled r times with a series of sampling pulses which occur one after the other at a period T = 1/f.sub.1. To determine the successive sets of multiplying coefficients this series of sampling pulses is each time shifted over a time distance T/r with respect to the previous series of sampling pulses.
If the filter to be realized is formed by an ideal low-pass filter having a cut-off frequency f.sub.1 /2, then the impulse response of this filter has the known form which can be mathematically represented by: ##EQU2## To determine the multiplying coefficients this impulse response is now sampled with sampling pulses which occur at a period T = 1/f.sub.1. The multiplying coefficients of the m.sup.th set a[ m,k] are now obtained by sampling this impulse response with a series of sampling pulses which can be mathematically represented by: ##EQU3##